Problem: Simplify the following expression: $y = \dfrac{10z^2 - 30z - 400}{z - 8} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $10$ , so we can rewrite the expression: $ y =\dfrac{10(z^2 - 3z - 40)}{z - 8} $ Then we factor the remaining polynomial: $z^2 {-3}z {-40} $ ${-8} + {5} = {-3}$ ${-8} \times {5} = {-40}$ $ (z {-8}) (z + {5}) $ This gives us a factored expression: $\dfrac{10(z {-8}) (z + {5})}{z - 8}$ We can divide the numerator and denominator by $(z + 8)$ on condition that $z \neq 8$ Therefore $y = 10(z + 5); z \neq 8$